Friction
Objectives
•
Calculate friction forces from equation
models for static, kinetic, and rolling friction.
•
Solve one-dimensional force problems that
include friction.
Assessment
1. A box with a mass of 10 kg is at rest on
the floor. The coefficient of static friction
between the box and the floor is 0.30.
Estimate the force required to start sliding
the box.
Assessment
2. A 500 gram puck is sliding at 20 m/s across a
level surface. The coefficient of kinetic friction
between the puck and surface is 0.20.
a. Draw a free-body diagram for the puck and
calculate the magnitude of each force.
b. How long will it take the puck to skid to a stop?
Physics terms
•
coefficient of friction
•
static friction
•
kinetic friction
•
rolling friction
•
viscous friction
•
air resistance
Equations
kinetic friction
static friction
rolling friction
Models for friction
The friction force is approximately equal to the
normal force multiplied by a coefficient of friction.
What is friction?
Friction is a “catch-all” term that collectively refers to all forces which
act to reduce motion between objects and the matter they contact.
Friction often transforms the energy of motion into thermal energy or
the wearing away of moving surfaces.
Kinds of
friction
Kinetic friction
Kinetic friction is sliding friction. It is a force that resists
sliding or skidding motion between two surfaces.
If a crate is dragged to the right, friction points left. Friction acts
in the opposite direction of the (relative) motion that produced it.
Kinetic friction
Which takes more force to push
over a rough floor?
Friction and the normal force
The board with the bricks, of course!
The simplest model of friction states that frictional force is
proportional to the normal force between two surfaces.
If this weight triples, then the normal force also triples—and
the force of friction triples too.
A model for kinetic friction
The force of kinetic friction Ff between two surfaces equals
the coefficient of kinetic friction μk times the normal force FN.
direction of
motion
But what is this coefficient of friction, μk?
The coefficient of friction
The coefficient of friction is a constant that depends on both
materials. Pairs of materials with more friction have a higher μk.
direction of
motion
The μk tells you how many newtons of friction you get per
newton of normal force. Do you see why μk has no units?
A model for kinetic friction
The coefficient of friction μk is typically between 0 and 1.
direction of
motion
•
When μk = 0 there is no friction.
•
When μk = 0.5 the friction force equals half the normal force.
•
When μk = 1.0 the friction force equals the normal force.
Calculating kinetic friction
Consider a 30 N brick sliding across a floor at constant speed.
What forces act on the block? Draw the free body diagram.
Calculating kinetic friction
Consider a 30 N brick sliding across a floor at constant speed.
What is the friction force on the brick if μk = 0.5?
Calculating kinetic friction
Consider a 30 N brick sliding across a floor at constant speed.
The force F needed to make the
board slide at constant speed
must also be 15 N.
Static friction
Static friction is gripping friction. It is a force that prevents
relative motion between surfaces in contact with each other.
• Without static friction between your
feet and the floor, you could not walk
or run. Your feet would slip.
• Without static friction between your
tires and the road, you could not start
or stop a car.
Static friction
Static friction prevents this crate
from sliding when pushed . . .
Static friction
Static friction prevents this crate
from sliding when pushed . . .
. . . until the pushing force is
greater than the maximum static
friction force available.
Static friction
How much static friction acts
• in case a?
• In case b?
Static friction
How much static friction acts
• in case a?
120 N
• In case b? 160 N
The crate is at rest so the net force
must be zero. The static friction
increases exactly as needed to
keep the box at rest.
Static friction
How much static friction acts
• in case a?
120 N
• In case b? 160 N
What is the maximum static friction
available?
Static friction
How much static friction acts
• in case a?
120 N
• In case b? 160 N
What is the maximum static friction
available? 200 N
Once the maximum static friction
is exceeded, the crate begins to
move.
A model for static friction
The maximum static friction force Ff between two surfaces is
the coefficient of static friction μs times the normal force FN.
direction of
applied force
•
When μs = 0 there is no friction.
•
When μs = 0.5 the maximum friction force equals half the normal force.
•
When μs = 1.0 the maximum friction force equals the normal force.
Calculating static friction
A 10 N board is at rest on a table.
How much force does it take to start
the board sliding if μs = 0.2?
Ask yourself:
What forces act on the block?
Draw the free-body diagram.
mg = -10 N
FN = +10 N
Calculating static friction
A 10 N board is at rest on a table.
How much force does it take to start
the board sliding if μs = 0.2?
The applied force F must be enough
to break the grip of static friction.
mg = -10 N
FN = +10 N
Calculating static friction
A 10 N board is at rest on a table.
How much force does it take to start
the board sliding if μs = 0.2?
• 2 N is the maximum force of static
friction available.
• 2 N is also the minimum force
needed to start the board moving.
mg = -10 N
FN = +10 N
Typical values of μs and μk
Which combination of materials
has the highest friction? lowest?
Why is it good that rubber on dry
concrete has such a high value?
How do you reduce the friction
between steel parts?
What do you notice about the
relative values of μs versus μk?
Typical values of μs and μk
These coefficients of friction are
only estimates, subject to ± 30%
or more uncertainty.
Actual experiments are needed
in any situation where an
accurate value is required.
Engaging with the concepts
In Investigation 5C you will
determine the coefficients
of friction between a
friction block and table top.
The investigation is
found on page 157.
Investigation
Part 1: Coefficient of static friction
Set up the stand and pulley near
a table. The string passing over
the pulley should act along the
centerline of the friction block.
Tie one end of the string to the
friction block and the other end
to the cup.
Investigation
Part 1: Coefficient of static friction
1. Set up the experiment. Measure
all masses to within 1 gram.
2. Add mass to the cup and record
the maximum mass at which the
block stays at rest.
Be sure to brush any dust or grit
from the surfaces before each trial.
Investigation
Part 1: Coefficient of static friction
3. Add more mass on top of the
block and repeat the experiment.
4. Add more mass on top of the
block and repeat the experiment
a third time. Record all
measurements in scientific
notation and correct SI units.
Investigation
?
?
?
How can you get the coefficient of static friction from
the measured masses?
Investigation: finding μs
When the block is on the verge of moving, the static friction
must equal the force from the weight of the hanging cup, m1g.
Investigation: finding μs
When the block is on the verge of moving, the static friction
must equal the force from the weight of the hanging cup, m1g.
The coefficient of static friction equals the ratio of the masses.
Investigation
Part 2: Coefficient of kinetic friction
Use the friction block arrangement
with the largest mass m2 (from part 1).
1. Adjust the mass of the cup
until the friction block has a
noticeable acceleration across
the table. Measure all masses
to within 1 gram.
Investigation
Part 2: Coefficient of kinetic friction
2. Measure the height h the cup
drops from its maximum
possible height directly under
the pulley.
Mark the table with tape so you
can start the block at the same
place each time.
Investigation
3. Release the friction block and measure the time it takes for
the cup to fall the distance h. Do several trials. Record all
measurements in scientific notation and correct SI units.
Investigation: finding μk
Step 1: Find the acceleration
from the height h and time t.
Let down be positive so that h
and a will both be positive.
Investigation: finding μk
Step 2: Find the net force on the system.
The total mass of the system:
The net force on the system:
system
boundary
Investigation: finding μk
Step 3: Find the force of friction
The weight of the cup speeds the
system up, but friction slows it down.
Rearrange the equation to solve for
the friction.
system
boundary
Investigation: finding μk
Step 4: Solve for μk.
system
boundary
Evaluating models
The scientific explanations or models for static and kinetic friction
use a constant value for each friction coefficient.
1.
Analyze these models for friction
by using the percentage variation
in your results among trials.
2.
Critique these models based on
your experimental testing.
3.
Evaluate the models by comparing
your experimental results to the
tabulated values of the
coefficients. How precise are the
models and coefficients?
Rolling friction
Many machines, such as cars and
bicycles, experience rolling friction.
The equation model for rolling
friction is similar to the model for
sliding friction.
Coefficient of rolling friction
Rolling friction comes mainly from slight deformations of the
wheel. It is typically much lower than static or kinetic friction.
Larger wheels tend to have lower coefficients of friction.
Viscous friction
Fluid friction is the largest source of friction for
cars, boats, and aircraft at speeds above 50 mph.
There are two main sources of fluid friction:
• the force required to push the fluid out of the way
• the resistance of the fluid due to viscosity
Viscous friction is complex. It depends on speed,
shape, and fluid properties.
Shape factors
The drag coefficient describes
how easily fluid flows around a
particular shape.
•
Blunt objects have high
drag coefficients.
•
Aerodynamic, streamlined
shapes have low drag
coefficients.
Viscosity
Viscosity describes a fluid’s resistance to flow.
Air has a very low viscosity.
Water also has a low viscosity
and pours readily.
Honey has a high viscosity
and pours slowly.
Assessment
1. A box with a mass of 10 kg is at rest on
the floor. The coefficient of static friction
between the box and the floor is 0.30.
Estimate the force required to start sliding
the box.
Assessment
1. A box with a mass of 10 kg is at rest on
the floor. The coefficient of static friction
between the box and the floor is 0.30.
Estimate the force required to start sliding
the box.
The required force is about 29 N.
Assessment
2. A 500-gram puck is sliding at 20 m/s across a level surface.
The coefficient of kinetic friction between the puck and
surface is 0.20.
a. Draw a free-body diagram for the puck.
Assessment
2. A 500-gram puck is sliding at 20 m/s across a level surface.
The coefficient of kinetic friction between the puck and
surface is 0.20.
a. Draw a free-body diagram for the puck.
direction of motion
Assessment
2. A 500-gram puck is sliding at 20 m/s across a level surface.
The coefficient of kinetic friction between the puck and
surface is 0.20.
a. Draw a free-body diagram for the puck
and calculate the magnitude of each
force.
direction of motion
Assessment
2. A 500-gram puck is sliding at 20 m/s across a level surface.
The coefficient of kinetic friction between the puck and
surface is 0.20.
b. How long will it take the puck to skid to a stop?
Hint: What is the acceleration of the puck?
direction of motion
Assessment
2. A 500-gram puck is sliding at 20 m/s across a level surface.
The coefficient of kinetic friction between the puck and
surface is 0.20.
b. How long will it take the puck to skid to a stop?
direction of motion